Emittance Theory for Cylindrical Fiber Selective Emitter

A fibrous rare earth selective emitter is approximated as an infinitely long cylinder. The spectral emittance, epsilon(lambda), is obtained by solving the radiative transfer equations with appropriate boundary conditions and uniform temperature. For optical depths, Kappa(R) = alpha(lambda)R, where alpha(lambda) is the extinction coefficient and R is the cylinder radius, greater than 1 the spectral emittance is nearly at its maximum value. There is an optimum cylinder radius, R(opt), for maximum emitter efficiency, eta(E). Values for R(opt) are strongly dependent on the number of emission bands of the material. The optimum radius decreases slowly with increasing emitter temperature, while the maximum efficiency and useful radiated power increase rapidly with increasing temperature.